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# hw10 - What is the efficiency Problem 47– Brushless DC...

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EE321 Spring 2009 Homework 10 Problem 44 – Back EMF A PMSM has a radius of 0.1 m and a length of 0.05 m. The conductor density of the a-phase of a PMSM is given by ) 4 sin( 200 sm as n φ = With no stator current, the B-field due to the PM on this machine may be expressed ) 4 sin( rm B = The mechanical rotor position is given by t rm 100 = θ Compute the voltage across the a-phase at t=0.1 s. Problem 45 – QD Transformation Starting with abcs T abcs cs cs bs bs as as i v i v i v P i v = + + = Show that ( 29 s s r ds r ds r qs r qs i v i v i v P 0 0 2 2 3 + + = Problem 46 – Brushless DC Operation from a Voltage Source A three phase brushless DC machine has the following parameters: = 3 s r , 10 = ss L mH, 17 . 0 = m λ Vs, 4 = P . It is operating from an inverter and the control is such that 100 = s v V (rms) and 0 . 0 = v . The load torque is given by 3 . 2 ) 200 / ( 2 rm l T ϖ = . Find the steady-state rotor speed in RPM, and the magnitude of the stator current.
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Unformatted text preview: What is the efficiency ? Problem 47– Brushless DC Operation from a Current Source Consider the machine in Problem 46, with the same load torque. Instead of being supplied from a voltage source, consider the situation if the machine is supplied from a current source (with all the current in the q-axis). Plot the rms current, rms voltage, and efficiency of the machine as the speed is varied from 0 to 4000 RPM. Problem 48 – Brushless DC Parameter Identification A three-phase brushless dc machine is open circuited, and is spun using a dynamometer. The a- to b- phase voltage measured from an oscilloscope if found to be sinusoidal. The waveform has a peak-to-peak voltage of 200 V, and a frequency of 82 Hz. What is m ?...
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